Easedrounded

Easedrounded is a term used in computer graphics and user interface design to describe a composite technique that blends motion easing with geometric rounding to produce smooth, natural transitions on shapes and paths. The core idea is to apply an easing function to the progress of an animation while simultaneously adjusting a rounding parameter, such as a corner radius or edge curvature, according to its own easing profile. This results in morphing shapes that not only move with eased timing but also change their edges in a gradual, visually coherent manner.

In practice, time t in the interval [0,1] is used to drive both the spatial and geometric aspects of a transition. An animation progress p is often defined as p = e(t), where e is an easing function (for example, a quadratic ease-in-out). The rounding radius r may be defined as r = r_max * f(t) or similar, with f chosen to produce the desired edge evolution. When coordinated, the pair of parameters yields a path or shape that finishes with a desired final geometry while exhibiting eased movement and rounded edges throughout the transition.

Applications include user interface morphing, such as transforming a rounded rectangle into a circle or adjusting the radius of corners during a button press, as well as vector shape morphing in graphic design and animation pipelines. The technique emphasizes synchronized timing and geometry to avoid abrupt changes in curvature.

See also: easing functions, rounded corners, Bézier curves, morphing, vector graphics.